Application of the Gauss' method to the stellar three body problem
type: Item
instance of: scholarly article
title: Application of the Gauss' method to the stellar three body problem
zbMATH Open document ID: 0900.70156
DOI: 10.1023/A:1008283513902
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1998-11-15T00:00:00Z
review text: The stellar three-body problem with two close stars and the third one located far away from two others is considered. It is supposed that the orbit of the third star is the Keplerian one. The Gauss' method which consists in replacing a gravitational attraction of the third star by the gravitational attraction of an infinitesimal non-homogeneous elliptic ring. Until now the analytic results were related with an elliptic ring of a small eccentricity. However, in general this is not valid when applied to the stellar problem, since the outer orbit is not necessarily almost circular. In the article an analytic method is developed to obtain not potential but the force vector for any value of eccentricity.
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 85A05
zbMATH DE Number: 1176771
zbMATH Keywords: celestial mechanics
zbMATH Keywords: stellar dynamics
zbMATH Keywords: three-body problem
zbMATH Keywords: multiple stars
zbMATH Keywords: elliptic integrals
author: Alberto Abad
author: Fernando Belizón
MaRDI profile type: Publication
full work available at URL: a:1008283513902
OpenAlex ID: W4252957363
description: scientific article; zbMATH DE number 1176771